1270 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



chosen, which is thin enough or thick enough to keep these critical fre- 

 quencies out of the band. 



Mode conversion from TEoi to the TEi,„ modes in serpentine bends is 

 not changed substantially by the presence of the dielectric coat. Gener- 

 ally these mode conversion effects decrease rapidly with the beat wave- 

 length. When the curvature varies slowly compared to the difference 

 in phase constant between coupled waves almost pure normal mode 

 propagation is maintained. 



v. MODE CONVERSION AT TRANSITIONS FROM PLAIN WAVEGUIDE TO THE 

 DIELECTRIC-COATED W^AVEGUIDE 



We consider a round waveguide, a section of which has a dielectric 

 layer next to the walls. A pure TEoi wave incident on this dielectric- 

 coated section will excite TE^m waves. For circular electric wave trans- 

 mission it is important to keep low the power level of the higher circular 

 electric waves which have low loss. 



In an evaluation of Schelkunoff's generalized telegraphist's equations 

 for the TEoi mode in a circular waveguide containing an inhomogeneous 

 dielectric^ S. P. Morgan describes the wave propagation in the dielectric- 

 filled waveguide in terms of normal modes of the unfilled waveguide. 

 The only restriction made in this analysis for the dielectric insert is 



\f\e-l\dS«l, (32) 



where S is the cross-sectional area of the guide. 



The dielectric-coated guide satisfies (32), and we may use the results 

 of Morgan's evaluation here. 



The round waveguide is considered as an infinite set of transmission 

 lines, each of which represents a normal mode. Along the dielectric- 

 coated section the TEom transmission lines are coupled mutually. The 

 coupling coefficient d between TEoi and one of the TEq^ waves is ob- 

 tained by taking Morgan's general formula and evaluating it for the di- 

 electric coat: 



V|Soi|8om 3 



We mtroduce this coupling coefficient into the coupled fine equations 

 (16). Since d/A^ « 1 for any of the coupled modes, the spurious mode 

 level at the output of the dielectric-coated section is given by (21), 



20 log 



10 



^2n 



^1 



on 1 2 (e' - l)poiPoml3~ 3 ,oA\ 



20 logic -^ ~ ^ — , 5 . (34; 



^ (/3oi - iSom) V^OllSom 



